# Slope-intercept form | Algebra I | Khan Academy

– [Voiceover] There’s
a lot of different ways that you could represent
a linear equation. So for example, if you
had the linear equation y is equal to 2x plus three, that’s one way to represent it, but I could represent this in
an infinite number of ways. I could, let’s see, I could subtract 2x from both sides, I could write this as negative 2x plus y is equal to three. I could manipulate it in
ways where I get it to, and I’m gonna do it right now, but this is another way of
writing that same thing. y minus five is equal to
two times x minus one. You could actually simplify this and you could get either
this equation here or that equation up on top. These are all equivalent,
you can get from one to the other with logical
algebraic operations. So there’s an infinite number of ways to represent a given linear equation, but I what I wanna focus on in this video is this representation in particular, because this one is a
very useful representation of a linear equation and
we’ll see in future videos, this one and this one can also be useful, depending on what you are looking for, but we’re gonna focus on this one, and this one right over
here is often called slope-intercept form. Slope-intercept form. And hopefully in a few minutes, it will be obvious why it
called slop-intercept form. And before I explain that
to you, let’s just try to graph this thing. I’m gonna try to graph it, I’m just gonna plot some points here, so x comma y, and I’m
gonna pick some x values where it’s easy to calculate the y values. So maybe the easiest is
if x is equal to zero. If x is equal to zero, then
two times zero is zero, that term goes away, and
you’re only left with this term right over here, y is equal to three. Y is equal to three. And so if we were to plot this. Actually let me start plotting it, so that is my y axis, and let me do the x axis, so that can be my x, oh that’s not as straight as I would like it. So that looks pretty good, alright. That is my x axis and let me mark off some hash marks here,
so this is x equals one, x equals two, x equals three, this is y equals one, y equals two, y equals three, and obviously I could keep going and keep going, this would be
y is equal to negative one, this would be x is equal to negative one, negative two, negative three, so on and so forth. So this point right over
here, zero comma three, this is x is zero, y is three. Well, the point that represents
when x is equal to zero and y equals three, this is, we’re right on the y axis. If they have a line going
through it and this line contains this point, this is
going to be the y- intercept. So one way to think about it,
the reason why this is called slope-intercept form is it’s very easy to calculate the y-intercept. The y-intercept here is going to happen when it’s written in this form, it’s going to happen
when x is equal to zero and y is equal to three, it’s gonna be this point right over here. So it’s very easy to
figure out the intercept, the y-intercept from this form. Now you might be saying, well it says slope-intercept form, it must also be easy to figure out the slope from this form. And if you made that conclusion, you would be correct! And we’re about to see
that in a few seconds. So let’s plot some more points here and I’m just gonna keep
increasing x by one. So if you increase x by
one, so we could write that our delta x, our change
in x, delta Greek letter, this triangle is a Greek letter, delta, represents change in. Change in x here is one. We just increased x by
one, what’s gonna be our corresponding change in y? What’s going to be our change in y? So let’s see, when x is equal to one, we have two times one, plus three is going to be five. So our change in y is going to be two. Let’s do that again. Let’s increase our x by one. Change in x is equal to one. So then if we’re gonna increase by one, we’re gonna go from x equals one to x equals two. Well what’s our corresponding change in y? Well when x is equal to two, two times two is four,
plus three is seven. Well our change in y, our
change in y is equal to two. Went from five- when x went from one to two, y went from five to seven. So for every one that we increase x, y is increasing by two. So for this linear
equation, our change in y over change in x is always going to be, our change in y is two when
our change in x is one, or it’s equal to two, or we could say that our
slope is equal to two. Well let’s just graph this to make sure that we understand this. So when x equals one, y is equal to five. And actually we’re gonna
have to graph five up here. So when x is equal to one, y is equal to, and actually this is a little bit higher, this, let me clean this up a little bit. So this one would be, erase that a little bit. Just like that. So that’s y is equal to four, and this is y is equal to five. So when x is one, y is equal to five, so it’s that point right over there. So our line is going to look- you only need two points to define a line, our line is going to like, let me do this in this
color right over here. Our line is going to look like, is going to look, is going to look something like, is going to look, let me see if I can, I didn’t draw it completely at scale, but it’s going to look
something like this. This is the line, this is the line, y is equal to 2x plus three. But we already figured out
that its slope is equal to two, when our change in x is one, when our change in x is
one, our change in y is two. If our change in x was negative one, if our change in x was negative one, our change in y is negative two. And you can see that,
if from zero we went, we went down one, if we
went to negative one, then what’s our y going to be? Two times negative one is negative two plus three is one. So we see that, the point
negative one comma one is on the line as well. So the slope here, our
change in y over change in x, if we’re going from between any two points on this line, is always going to be two. But where do you see two
in this original equation? Well you see the two right over here. And when you write something
in slop-intercept form, where you explicitly solve for y, y is equal to some constant
times x to the first power plus some other constant,
the second one is going to be your intercept, your y-intercept, or it’s going to be a way to
figure out the y-intercept, the intercept itself is this
point, the point at which the line intercepts the y axis, and then this two is going
to represent your slope. And that makes sense because
every time you increase x by one, you’re gonna
multiply that by two, so you’re gonna increase y by two. So this is just a, kinda
of a get your feet wet with the idea of slope-intercept form, but you’ll see, at least for
me, this is the easiest form for me to think about what the graph of something looks like, because if you were given another, if you were given another linear equation, let’s say y is equal to negative x, negative x plus two. Well immediately you say, okay look, my yintercept is going to be the point zero comma two, so I’m
gonna intersect the y axis right at that point, and
then I have a slope of, the coefficient here is
really just negative one, so I have a slope of negative one. So as we increase x by one, we’re gonna decrease y by one. Increase x by one, you’re
gonna decrease y by one. If you increase x by two,
you’re gonna decrease y by two. And so our line is gonna
look something like this. Let me see if I can draw
it relatively neatly. It’s going to look something, I think I can do a little
bit better than that. It’s ‘cus my graph paper is hand drawn. It’s not ideal, but I think you get, you get the point. It’s gonna look something like that. So from slope-intercept form, very easy to figure out
what the y-intercept is, and very easy to figure out the slope. The slope here, slope
here is negative one. That’s this negative one right over here, and the y-intercept, y-intercept is the point zero comma two, very easy to figure out ‘cus essentially that gave you the information right there.

## 100 thoughts on “Slope-intercept form | Algebra I | Khan Academy”

1. Glanton Seann says:

I highly appreciate the help but I guess im just dumb BECAUSE I STILL DONT GET IT T-T

2. Glanton Seann says:

I miss pre-k where we could just take naps

3. Alex Martel says:

thanks for the explanation! hopefully this will help me with EQAO

4. Alex Martel says:

after watching this video, I came back to class 500% smarter on the subject

5. Shy Guy says:

TUTOR ME

6. knee's bees says:

my whole math class failed a test on this and now we have to retake it, wish me luck

7. Kamrul Islam says:

And The x intercept is -1.5

8. Aarav Srivastava says:

This couldn't be possible there are 3.2k likes and I didn't get even a single thing he told😢😢

9. 0nlyoneTyi duh says:

My Brain 🧠 hurts

10. _AloneSonance_ says:

I've scrolled way to far down into my YouTube recommend videos again

11. Taliah Bannister says:

i understand a little bit more

12. nabeer chowdhury says:

It is explained so beautifully… In other videos, they tend to confuse learning with memorization. But in this your teaching method is really superior to the rest

13. Technical Gamer414 says:

Hats off ! The way you explained it was amazing. I understood this chapter which i could understand normally in 1 hour in 5 minutes because of this video

14. TryHardDieHard says:

I have test tomorrow, I need to cram!

15. Sebasthian Ramos Barreto says:

this makes no sense

16. Rami Jaouhari says:

Rise Over Run

17. My super dead channel says:

I find it funny how he used the exact equation I’m working on 😂

18. BiscuitBurger says:

Quick maths

19. Andrew Allen says:

I feel like this is just another way to stop people from being successful. Somebody could be a great doctor and terrible at algebra, something that you don't need for that career. I dont see them making math teachers run a 40 in 4.30 seconds. Why because most can't but could still be good math teachers. I also feel like it's a way for the colleges to make money, by forcing extra classes on people.

20. slope. says:

This is completely different from what my teacher taught me!

21. D T says:

I am back to re-learning this after 18 years, same thing again. Gosh…

22. Md Yusuf says:

It's driving me nuts

23. out of luck says:

Why zero

24. smelly c a t .-. says:

I’m having a break down. I don’t get it and CHECKED

25. Xerk 450 says:

Where can I use this in life

26. Без поклонников Sans Fans says:

How would you find the y-intercept when x isn't 0, like it starts on like 3 and y starts at 6 or something like that?

27. Moon Tide says:

The only reason why there are thumbs down is it is eather summer for them or they dont get it…. I mean i dont get it but i dont thumbs down the video. It helped me a little i just dont get it. Oof ima hands on person can u tell?

28. Snister says:

I have a math test after tomorrow send help; c

29. Sam Bagley says:

He sounds like Ross from Friends…

30. Isabel Tanner says:

Finally after 2 years i under stand this

31. Kayla Sarceño says:

Anyone here because they have a test tomorrow and is studying last minute. Cries in Algebra

32. Fiorella Caro says:

My STAAR (state test) is today, and I can’t seem to find any way to learn this.

33. Veda Merrell says:

l uderstand it all ontil 6:11.

35. Subhash Chaganti says:

Thanks for the video!! But Voice is very feeble!

Whenever he explains something and I get it I get really happy

37. Genevieve says:

Thank you

38. Krishna Choppara says:

F

39. BucketOGravy says:

Great video! Helped with my final

40. unknown user says:

how do u know what the x is???????!1!?1/!?1/!?AAAAAAAAAAAAAAAAAAAAAAAAAAA

41. Katerina Pierce says:

I’m confuzzled

42. El Chapo alv says:

I got lost at 0:01

43. The Tea Sweetie says:

Thank you! I have horrible teachers so this helped a lot.

44. James Ambush says:

I under that A squared plus B squared equals C squared, but can you explain something to me?

This is my own hypothetical math problem I'll be using to explain my confusion.

If Line A and Line B are parallel and the distance between line A and Line B is 10 meters but you travel at a 45 degree angle from Line A, how does it not take 15 meters to reach Line B? For some reason my mind jumps to it taking time and a half distance to travel between two parallel points when traveling at a 45 degree angle. I know this isn't true but can you explain in detail why besides A squared plus B squared equals C squared?

45. Sivaram kumareswaran says:

Algebra is trying to kill me.

46. Sivaram kumareswaran says:

Watch this if you hate algebra: https://www.khanacademy.org/math/algebra/introduction-to-algebra/overview-hist-alg/v/the-beauty-of-algebra

47. Roronoa Zoro says:

This isn’t helping that much I still don’t understand what the “m” is for

48. Lexy L says:

The thing is why didn’t he just tell you in the first place that the M value or 2 in this equation is the slope and B or 3 is the y intercept and then show you

49. Lexy L says:

This is gonna help so much with my exam at Prufrock Prep tomorrow, thanks!

50. Remnants says:

The amount people who can't understand something this basic makes me think i'm in a weird city.

51. Colin Moore says:

Algebra 1 Bois wya

52. Mr.Deksam says:

Dude im so lost

53. Mountain Lion says:

I see all of the comments saying, "I'm having a mental breakdown." Trust me though. I am in Kumon H 155 math, which means I am getting into grade 9, and 10 mathematics. Yet, I am only a grade 7.

Also studying grade 10 – college physics. If I can do it, I think a lot of people can!

The most easy way by which a math can be solved is shown by this video completely. Really felt benefited. Thanks. & keep continuing.

55. Who says:

Algebra II this year, I’m doomed

56. Saleina Garcia says:

57. Thomas Williams says:

is this formula universal for slope intercept?

58. KV Dalisay says:

putangina pano?

59. aarohi craft says:

Algebra comes from a term from Arabic word

60. Abhinandan Chandran says:

JAC students make this comment blue

61. MarkGH says:

Massive shoutout to SinisterGH for leading me here. Truly one of the greatest (and most underrated) FCs of the clone hero age. Keep up the great work Sal!

62. Guacardo says:

I’m gonna cryyyy I have a test tmrw and I don’t understand

63. Abigail McMillin says:

Thank you so much. I'm a very non mathematical person I'm all language and Grammer type things and I'm struggling so much.

64. MsCankersore says:

That negative 1 at the end, shouldnt it have gone the other way (left) instead?

65. Sandwich Cake says:

I have a test today and I don’t understand this at all

I don’t understand point slope form either

This is too anyone who disliked this helpful video. I hope your Minecraft dog dies.

67. Animation Space says:

68. wholesome minecraft Parrot says:

i still don’t understand 😗✌🏼

69. umair alvi says:

So intuitive.

70. Emma Duran says:

y=mx+b

Lol that’s all you need to do

71. Gabriel Ramos says:

im good at math but I hate it 🙁

72. Nam Nam says:

Me too

73. Dottie Theclown says:

honestly, I still get a mental breakdown with this stuff

74. Sienna Olen says:

Dear god im going to fail my test

75. MEGA TRUMPER says:

it feels like no one has ever head of a CALCULATOR

76. Roy Luo says:

same and I have this for homework except I was given the graph and have to find the slope-intercept form

77. sophia martin says:

Honestly, being a high school dropout seems like the best option at this point.

78. Clue ღツ says:

THIS IS EASYYY

79. Julie MacKaben says:

Ummmmmm I don't speak math.

80. TURTLE BOI says:

Wait till you study quadratic functions

81. Amy :3 says:

Ok, I’m 11 years old and I don’t get this…but I should be getting it at this age

82. Brandon and friends says:

Who else is good at everything except algebra?

83. Cat.Toss.Animated says:

Dude i thought was finna fail thank youuuuuu

Great teaching skills 👌🏻👌🏻
BTW what software are you using

85. Audrey Ivy43 says:

currently balling my eyes out and watching while watching this 😚✌🏽😍

86. zuyi says:

i gotta do this and i’m in 7th grade pre-algebra

87. August Wilde says:

G

88. Rocky’s Playhouse says:

I have a 64% in math adv, I’m gonna get kicked out of my accelerated classes, I have 8 days to bring it back up,
im screwed

89. Kai Alosno says:

Bruh I’m in middle school this is hard

90. Chris Taylor says:

Yeah, you lost me with the second one. The first example was great then you did something weird with the second one 🤦🏾‍♂️

91. luxurybargains market says:

You mean a line segment, Mr.Sal

92. luxurybargains market says:

I love mathematics

93. Animemetric says:

This guy is the reason I'm not failing.

94. Baba yaga says:

So will y intercept always be (0,x)?

95. Wils The Limit says:

I am dreading my test on Friday

96. NATIONBOYJAMEION says:

Who has Exams Monday ☹️

97. Jiren The Grey says:

You just helped my sis with this vid thank you

98. Sophia Jafar says:

I need khan academy and hope it stays free. My teacher uses it to give us extra credit like a lot and I went from a D to an A in my math class because I did 4 worksheets on khan academy.

99. Flat cheese says:

When your teacher tells you have the test in two days and didn’t teach you anything in class

100. Tresyy Tresylia says:

im a chemistry student. tell me again why do i have to study maths in uni……..